### Περιεχόμενα

 INTRODUCTORY REMARKS ON SOLIDS SURFACES LINES 1 and 5 AXIOMS 7 EUCLIDS PROPOSITIONS I TO IV 14 EUCLIDS PROPOSITIONS IX TO XII 24 EUCLIDS PROPOSITIONS XVI AND XVII 30 PROPOSITION 31 EUCLIDS PROPOSITIONS XXIX TO XXXIII 44
 EUCL V 25 240 EUCL V c 241 EUCL V E 242 INTRODUCTORY REMARKS 243 DEFINITION I 244 MISCELLANEOUS EXERCISES ON PROPS I TO VI 255 EUCLIDS PROPOSITION VII 256 EUCL VI 9 258

 ON THE EQUALITY OF RECTILINEAR FIGURES 57 INTRODUCTORY REMARKS 77 PROPOSITION 84 EUCLIDS PROPOSITIONS VII TO XIV 93 DEFINITION VII 128 EUCLIDS PROPOSITIONS XI To XV 136 EUCLIDS PROPOSITIONS XXVI TO XXIX 159 EUCLIDS PROPOSITIONS XXIII AND XXIV OF BOOK III 175 APPENDIX TO BOOKS I IV 198 II 211 CONTAINING THE PROPOSITIONS MOST FRE 221 ON PROPORTION BY INVERSION ALTERNATION 227 EUCL V 233 CONTAINING THE PROPOSITIONS TO WHICH NO REFERENCE IS MADE IN BOOK VI Pp 235 to 235 EUCL V 6 236 EUCL V 17 237 EUCL V 19 238 EUCL V 23 239
 EUCL VI 10 259 EUCL VI 11 260 EUCL VI 12 261 EUCL VI 8 262 DEFINITION IV 264 EUCLIDS PROPOSITIONS XIV TO XIX 265 EXERCISES ON PROPOSITION XIX 274 EUCL VI 21 275 EUCL VI 20 276 EUCL VI 31 278 EUCL VI 22 280 PROPOSITION B 284 EUCL VI 25 290 INTRODUCTORY REMARKS 307 EUCL XI 3 313 MISCELLANEOUS EXERCISES ON BOOK XI 334 PAPERS ON EUCLID BOOKS VI AND XI SET IN THE CAM 342

### Δημοφιλή αποσπάσματα

Σελίδα 89 - To divide a given straight line into two parts, so that the rectangle contained by the whole, and one of the parts, may be equal to the square of the other part.
Σελίδα 168 - IF from any point without a circle two straight lines be drawn, one of which cuts the circle, and the other touches it ; the rectangle contained by the whole line which cuts the circle, and the part of it without the circle, shall be equal to the square of the line which touches it.
Σελίδα 7 - If a straight line meets two straight lines, so as to make the two interior angles on the same side of it taken together less than two right angles...
Σελίδα 40 - If two triangles have two angles of the one equal to two angles of the other, each to each, and one side equal to one side, viz. either the sides adjacent to the equal...
Σελίδα 23 - To draw a straight line perpendicular to a given straight line of an unlimited length, from a given point without it.
Σελίδα 106 - To draw a straight line through a given point parallel to a given straight line. Let A be the given point, and BC the given straight line ; it is required to draw a straight line through the point A, parallel to the straight hue BC.
Σελίδα 178 - The angle in a semicircle is a right angle; the angle in a segment greater than a semicircle is less than a right angle; and the angle in a segment less than a semicircle is greater than a right angle.
Σελίδα 46 - IF a straight line fall upon two parallel straight lines, it makes the alternate angles equal to one another...
Σελίδα 285 - Wherefore, in equal circles &c. QED PROPOSITION B. THEOREM If the vertical angle of a triangle be bisected by a straight line which likewise cuts the base, the rectangle contained by the sides of the triangle is equal to the rectangle contained by the segments of the base, together with the square on the straight line which bisects the angle.
Σελίδα 91 - In every triangle, the square of the side subtending either of the acute angles is less than the squares of the sides containing that angle, by twice the rectangle contained by either of these sides, and the straight line intercepted between the perpendicular let fall upon it from the opposite angle, and the acute angle.